Question

Quantitative relationship between entropy and number of microstates the Boltzmann equation where k is the Boltzmann constant per molecule (particle), 1.38 × 10 23 J/(K-particle). From this equation the entropy change, ΔS, for a system can be related to the change in the number of microstates as Wfinal initial where Wfinal in the final number of microstates and Winitial is the initial number of microstates.

A gaseous system undergoes a change in temperature and volume. What is the entropy change for a particle in this system if the final number of microstates is 0.465 times that of the initial number of microstates? (units is J/K.particle)

Answer 1

dS = k*ln(Wfinal / winitial)

k = 1.38*10^-23

Wfinal = 0.465 Winitial

Winitial = Winitial

therefore

dS = k*ln(Wfinal / winitial)

dS =  1.38*10^-23*ln(0.465 Winitial / winitial) = -1.0566*10^-23

dS =  -1.0566*10^-23 J/particleK